GridLAB-D (GLD) is an agent-based platform, developed by researchers at Pacific Northwest National Laboratory, that permits users to accurately simulate the state dynamics of power distribution systems at time scales ranging from sub-seconds to years. The purpose of this study is to present, in careful comprehensive form, a complete analytical state-space control representation for a version of the GLD Household Equivalent Thermal Parameter Model as support documentation for model users. This model is a physically-based implementation of a household with multiple price-responsive and conventional appliances whose thermal dynamics are determined over successive days by resident appliance usage and external weather conditions.